There is nothing more quintessential to math than precision. Without it, solutions to problems are impossible. After all, unless you dive into the more specialized realms of mathematics, you are unlikely to be faced with ambiguity. In short, at the level of everyday math, ‘maybe’ is simply not an answer. In this article, we explore this concept in its entirety.
What is precision in math?
Precision refers to a concept that is often used in mathematics, science, engineering, and technology. It is defined as the closeness of agreement between repeated measurements of a quantity.
For example, the weight of an object measured five times is closer to 3.2 kilograms than 2.8 kilograms. This difference is called imprecision. A person might say, “I weighed my apple three times and got 3.2 kilograms each time.” This would suggest that the level of precision is high and there is minimal lost precision.
What is arbitrary precision arithmetic?
Arbitrary precision arithmetic is an extension of the real number system in mathematics which allows for the use of nonstandard numbers, usually denoted by lowercase letters like p and q. Arbitrary precision arithmetic operations allow for calculations using an infinite number of digits in each base so that any desired precision can be achieved at no extra cost.
Arbitrary precision integers are utilized in computer science in order to allow arbitrary precision computation to go beyond the limits of the computer size. You therefore get nonterminal decimal digits, allowing the computation to transcend regular computing mathematical operations. While understanding arbitrary precision integer numbers is not necessarily something you will need in high school, you will need to understand these symbolic computation concepts if you choose to pursue higher mathematics or any type of career in the computing industry.
What is the difference between precision and accuracy?
Accuracy refers to how closely a measurement matches a true or accepted value while precision refers to how consistent measurements of an object are. Approximate values for precision are independent of both accuracy and stability.
That means that it is perfectly acceptable to have very high accuracy, but low precision–in other words, your measurements may vary greatly from one another, but they will all be fairly close to the correct answer. Conversely, a set of measurements could have very poor accuracy–in other words, a lot of errors–but good precision with all values being pretty much identical.
What are repeatability and reproducibility?
Repeatability is the variation arising in repeated measurements taken within a short period under identical circumstances. This is usually expressed as standard deviation. If you want to know how repeatable something really is, just multiply the standard deviation by three.
Reproducibility is the variation in repeated measurements taken over a long period among different instruments and operators. It is often expressed as a coefficient of variance. To find out how reproducible something really is, just divide the coefficient of variance by three. If you want to measure precision, think about what happens when you take measurements repeatedly. You might end up getting a range rather than a single figure.
Why is precision important in math?
Math is used in our everyday lives and, by default, so is precision. There are various reasons as to why precision is so important:
- It gives you correct measurements
- It allows for the creation of specific formulas
- It ensures that correct medical dosages are given
- It makes sure that correct results are achieved in scientific investigations
What is a bias in math?
When something is inherently wrong with a reading, it is referred to as a bias. When we measure something multiple times and all results are similar, they could all be wrong due to an inherent flaw within the measurement process itself. Such flaws can occur due to human error, such as incorrectly calibrated equipment or incorrect assumptions made during data collection. Such errors lead to bias, where all measurements are off by the same value.
How do you find precision in math?
Calculate the range
Work out the highest and lowest measured value by arranging your data in ascending numeric order. Next, work out the average. If your numbers are 2, 5, and 4, you’ll arrange them in descending order so that you have 2, 4, and 5. Then, calculate the range of the highest and lowest values:
5 – 2 = 3
Report the result as the mean plus or minus the range, including the mean if appropriate. To calculate the mean of the example above, all you need to do is add 2, 4, and 5 and divide by the amount of numbers in the list, so three. You would therefore end up with:
2 + 4 + 5 / 3 + = 3.67
Derive the average deviation
Calculate the absolute difference between each value and the mean. You need to determine how far each value is from the mean. Subtract the mean from each value. It does not matter whether the value is above or below the mean or if it comes out as a decimal number… it probably will. Simply take the positive value of the subtracted result. If we use the same example as the one above, our absolute deviations are:
1.67 (2- 3.67), 0.33 (4-3.67), 1.33 (5- 3.67)
Add the absolute differences together to get the mean using the same method that was used to obtain the mean above. Add them up, and divide by the total number of items. In this case, you would perform the calculation as follows:
1.67 + 0.33 + 1.33 / 3 = 3.33
How to solve a problem in mathematics
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